The general, explicit and formally closed expression of arbitrary n-times Foldy-Wouthuysen transformations is clearly and strictly derived out. It is proved that if transformed Hamiltonian needs to be approximated to the order 1/m^K or mv^2K when to involve the orders of the operators, then to make N = [(K + 1)/2]-times Foldy-Wouthuysen transformations is just enough ( “[...]”means to take the part of integer). An example in non-relativistic quantum chromodynamics is given.

Quantum cryptography allows the establishing of a highly confidential sequence of random bits between two parties who share no secret information in advance. Its security is guaranteed by the basic laws of quantum mechanics rather than mathematical difficulty. An experimental system based on a novel protocol for quantum cryptography using only two nonorthogonal photon polarization states is implemented. The photon sources are two semiconductor laser diodes operated at 680 nm, their light pulses which are heavily attenuated to far below one photon per pulse are employed to encode the key. Gated single photon detection technique is used to minimize the dark count effect of the photon multiplier tube. Key establishing rate of 40 b/s and error rate of 2.1 % are obtained. Compared with other systems, our system has the simplest experimental setup.

The thermodynamical entropy of the general four-dimensional static spherically symmetric black hole is obtained by using the Euclidean path integral approach of Gibbons-Hawking, and its statistical-mechanical entropy is calculated according to the brick wall model of ’t Hooft. It is shown that the two entropies are not identical in general and the difference between them depends on the area of the horizon and the Ricci scalar curvature on the event horizon.

In the study, a bistable system is driven by additive colored noise and multiplicative colored noise, whose correlation is of an exponential farm. When the noises are correlated, it is found that the system undergoes a reentrant transition as the correlation strength between noises or multiplicative noise intensity changes, while there is no such phenomenon as the additive noise intensity or the time of correlation changes. No reentrant transition exists when the noises are uncorrelated.

In this letter the scaling properties of the period-adding sequences in a so-called “multiple Devil’s staircase” are reported. It is certified both analytically and numerically that the width of the i-th phase-locked plateau in a sequence scales as In |Δe(i)| ∝ i, and the position of the plateau scales as In |e_∞ -e_i| ∝ i. These properties are qualitatively different from those of the period-adding sequences in conventional Devil’s staircases.

The nonlinear and the exact control of chaos is deduced. Using these methods we achieve a simultaneous and instantaneous control of the scheduled unstable 2^kp points for the logistic and the Henon map. The derivatives needed in the nonlinear method have been evaluated experimentally from the time series x_n, without the pre-knowledge of the function f(x). The difficulty confronted in the optimum control may be overcome by introducing the nonlinear control.

The hexadecapole deformation parameter β₄ of the rare-earth and actinide nuclei is investigated in the framework of the sdg interacing boson model. An explicit relation between the geometric hexadecapole deformation parameter β₄ and the intrinsic deformation parameters ε₄ , ε₂ are obtained. The deformation parameters β₄ of the rare-earths and actinides are determined without any free parameter. The calculated results agree with experimental data well. It also shows that the SU(5) limit of the sdg interacting boson model can describe the β₄ systematics as well as the SU(3) limit.

In order to clarify whether statistical or dynamical treatments for emission of intermediate mass fragments (IMFs) will be needed in the intermediate energy heavy ion collisions, the measured angular and energy distributions of IMF (3≤ Z ≤6 ) in 25 MeV/n ⁴⁰Ar+^natAg were analyzed by means of statistical calculation code GEMINI and quantum molecular dynamics code (QMD). While the angular distribution calculations with GEMINI code are not compatible with the experimental ones, the QMD calculations for inclusive angular distributions and energy spectra of IMF are in good agreement with the measured ones.

The Schrödinger equation of two ultracold ions confined in xy plane of the Penning trap is exactly solved and the analytical form of the wave function of the system is obtained. A numerical calculation for a continued fraction presents the relation among the beigenenergies, the Coulomb interaction and the azimuthal number.

A U(2) algebraic model is used to explain the stretching and bending vibrational spectrum of methane, where the interactions between the stretching and the bending modes are taken into account. This model provides good fits to the experimental vibrational eigenvalues with the smaller standard deviations of 9.57 and 9.08 cm^-1 than those in other published algebraic models.

In the frame of quantum defect theory, the state-testate dielectronic recombination rate coefficients of Fe²⁵⁺ ion are calculated by a simple relativistic configuration interaction method. The calculated results are further expressed with a two-parameter fitting formula, and then the dependence of fitting parameters on radiative decay final channel is studied.

It is found that a novel drift term, purely induced by cross correlation between multiplicative and additive noises, in the one-dimensional Langevin equation for a single-mode laser intensity has a significant effect on the intensity statistical properties near and below threshold, and when colored multiplicative noise is involved. This term makes the laser intensity fluctuations lower but effective eigenvalues larger for positive noise cross correlation.

Tunalbe coherent extreme ultraviolet radiation has been produced in nitrogen by third harmonic generation (THG) processes enhanced by two-photon resonance with the a¹II_g(v' = 1) state and three-photon resonance with the c'₄ ¹Σ⁺_u(v' = 1) state, respectively. The highly resolved THG spectra imply that THG can be used to probe the higher excited states and to detect the rotational population of a molecular gas.

A step index-type Nd³⁺-doped polymer optical fiber (POF) was prepared by using bulk polymerization of solution of Nd³⁺-octanoate (NOA) and methyl and methacrylate. A method of wide-angle x-ray diffraction was used to measure the solubility of NOA. In a high concentration Nd³⁺ doped POF, a residual absorption at 810nm could not be saturated, which is attributed to the high clustered ion rate in the Nd³⁺ POF. A model based on the rate equations to infer the clustered ion rate by the measurement of transmission is presented.

The bound state is one of the elemental localized excitations in a parametrically driven systems. In the molecule-like structure, the two identical solitons can interact with each other as a classic “oscillator”. Here the dynamics of two interacting bound states is explored by both experiment and computation. The experiment reveals several important dynamical features, in particular, the polarity ordering rule that determines the stability of a compound structure, and the synchronization in the coupling pairs of opposite polarity which leads to a symmetric and harmonic spatiotemporal oscillation. All these interesting phenomena are numerically simulated with the parametrically driven, damped nonlinear Schröding equation, and their nonlinear dynamics is further concluded as a stability diagram in parameter space.

A new method for solving elasticity problems of some planar quasicrystals is presented. The set of partial differential equations for the phonon and phason displacement components is reduced to a single higher-order equation by introducing a displacement function. A general solution formulation is suggested. As an example, the elastic field caused by a dislocation in planar quasicrystals of point groups 5 m , 10, and 10mm is calculated.

Based on not only the ideas of phenomenological investigations about the internal friction of crystalline materials but also the studies on the internal friction laws of noncrystalline materials during structural relaxation processes in recent years, the method of making relaxation cell is put out. In the method, traditional mechanics parameter model and two-level model are unified, so phenomenological studies on the internal friction of noncrystalline materials during structural relaxation processes are made and a new relaxation law is formed.

In situ high pressure energy dispersive x-ray diffraction experiments have been carried out on CsBr by using diamond anvil cell device with synchrotron radiation source. The maximum pressure is 115 GPa. The structure of CsBr is changed from simple cubic phase to tetragonal phase at pressure about 53 GPa, marked by the splitting of its strongest diffraction line (110). At pressure above 98GPa, the color change of CsBr from transparent to red-brown was observed. No pressure-induced transition from insulator to metal is found at higher pressure up to 115GPa.

Within a movable and orientable rigid rotor model, four interaction potentials of solid deuterium (hydrogen) system from combinations of two isotropic and two anistropic parts are tested by the path integral Monte Carlo method in a constant-pressure ensemble. With the best one of the potentials, the equation of state of deuterium is quantitatively in agreement with the experimental data. For understanding the quantum nature of the solid, the energies of the system at different temperatures are also calculated, the results show strong zero-point motions exist in the solid. As would be expected, the quantum corrections to both the rotational and the translational kinetic energies decrease with increasing temperature, and increase with pressure.

C₆₀ single crystals oriented at [111] about 1 μm in size, were grown in C₆₀ film on NaCl (001) substrate. Bilayer films of nickel, gold, silver, and indium over C₆₀ on NaCl substrate prepared by vacuum deposition method were studied with a transmission electron microscope. It was found that for different kinds of metals, their nucleation and growth characteristics on C₆₀ (111) surface are quite different. This phenomenon is mainly attributed to different activation energies of the four metals. Analyses of the experimental results indicate that the activation energies of Ni, Au, Ag, and In adatoms on C₆₀(111) surface change in a descent order.

Vertical transport I-V relations of type-I GaAs/A1As superlattices with doped wells and weak coupling between wells at 77K were investigated with quasistatic and dynamic method. Spontaneous current oscillations are also investigated. The domain formation time 70 ± 30 ns is directly measured. By using discrete-tunneling model, the key parameters of the relation between tunneling current and the bias between adjacent wells were quantitatively determined from the experimental data.

Based on the two-band model and free-electron approximation, a treatment of the magnetoresistance (MR) and interlayer exchange coupling (IEC) for ferromagnetic/nonmagnetic/insulator (semiconductor)/ferromagnetic tunnel junctions is presented. It is found that properties of the junctions are intermediate between tunnel junctions and metallic magnetic multilayers. The MR and IEC are all the oscillatory functions of the thickness of nonmagnetic layer. The results have potential in designing spin-polarized tunneling devices with large field-sensitivity.

The Raman scattering in Zn_0.74Cd_0.26Se/ZnSe superlattices under hydrostatic pressures up to 4.53 GPa at room temperature has been studied. The pressure-dependences of the ZnSe-like LO-phonon (LO_b) and the Zn_0.74Cd_0.26Se-like LO-phonon (LO_w) have been obtained. At 2.7GPa, the pressure-coefficients of both LO_b and LO_w phonon energies increase abruptly The 2LO_w-phonon resonance has been observed at 1.82GPa with 488.0nm excitation for the Zn_0.75Cd_0.25Se/ZnSe superlattices.

The photoluminescence of some platinum (II) complexes of aromatic α-diimines and pyridine-2-thiolates is enhanced upon incorporation into the polymer matrices polymethmethylacrylate (PMMA), polycarbonate, and polystyrene. Some applications of the platinum (II)-PMMA films as luminscent sensors reported. When platinum (II)-PMMA films are in ethanol solutions with different chloroform concentration, there is a systematic decrease of emission intensity with increasing chloroform concentration and the variation follows a Stern-volmer relationship.

We have studied the effects of γ-ray irradiation on electroluminescence (EL) from Au/extra thin Si-rich SiO₂ film/p-Si Structures. After γ-ray irradiation, for the structure with a 600°C annealed Si-rich SiO₂ film a new blue EL band with a peak at around 480nm was observed, and for the structure with a 300°C annealed Si-rich SiO₂ film the red EL band shifts from 670 to 660nm and its intensity and full width at half maximum increase pronouncedly. The experimental results demonstrate that the defects induced by γ-ray irradiation are responsible for the blue EL band as well as for the variations of the red EL band.

GaP nanocrystals were synthesized by both the organic solvent reflux and high temperature high pressure benzene thermal synthesis methods. The effect of organic solvent on the optical absorption properties of GaP nanocrystals were studied. The results show that crystal grains of the sample synthesized by the latter method have better quality and uniformity. The solvents which consist of polar molecules and form strong chemical bonds with Ga atoms cause obvious redshift of the absorption spectra of GaP nanocrystals. The absorption spectra redshift much more if the solvent molecules have π electrons which involved in the formation of complex bond between Ga atoms and solvent molecules.

Massive stars often tend to be in cluster when they form in molecular clouds, and bipolar molecular outflows occur during the forming process of stars. On the basis of newly observed bipolar molecular outflows associated with massive stars, three properties are proposed to statistically identify massive stars whether in cluster or not as the driving engines of the flows. For clustering massive stars with some exceptions, their outflow collimation factors are generally poor and less than two, and the correlations of the flow momentum rate and the mass flow rate with the central source bolometric luminosity deviate the ones for selected well-resolved 16 flows.